Boyce said police received more than 250 leads from the public. "Each one was vetted painstakingly by detectives," he said.
Over the past 10 days or so, one of those tips led detectives to the home Lewis shared with his mother in East New York, a Brooklyn neighbourhood on the Queens border, just to the west of Howard Beach.
Boyce said detectives first spoke to Lewis on Thursday night, and he freely gave up a swab of his DNA.
It was taken immediately to the medical examiner, Boyce said. "Within two days, we had a hit."
Police say they do not believe he knew Vetrano. Lewis told police he strangled the New York jogger simply because he was in a bad mood.
"I was angry. I had some issues at home. I just lost it. When I saw her, I just hit her and kept hitting her. I hit her and choked her," said the unemployed Lewis, according to New York Post sources.
Police sources said that in 2011 Lewis "wanted to bring a knife to school to stab all the girls". He was just 15 years old when he told a teacher's aide of his violent wishes, according to the sources.
Lewis didn't enter a plea or say anything at his hearing, but Vetrano's mother, Cathie Vetrano, leapt to her feet and cursed Lewis as the hearing was winding down.
"A savage murderer! He f***ing murdered my daughter, my beautiful innocent daughter! Now your nightmare begins!" she screamed.
"He's a demon! He should be in hell and burn in hell!"
Lewis told detectives that he happened to cross paths with Vetrano on a path inside Spring Creek Park while walking from his Brooklyn home to get something to eat in Howard Beach
"You gotta remember, Karina helped us identify this person," Boyce said, referring to evidence that was processed more than six months ago when Vetrano's body was discovered. "She had the DNA under her nails, she had touch DNA on her back, and there was more DNA on the cellphone."
"We're satisfied that we have a solid case," Queens District Attorney Richard Brown said at the news conference.
The arrest comes days after the family held a rally to try to renew interest in the case on the six-month anniversary of Vetrano's death.
Vetrano frequently went running with her father, Phil, a retired firefighter. But her dad, who was reportedly dealing with back pain, didn't join his daughter on the evening of August 2.
When she didn't come back from the run, Phil Vetrano grew worried.
"Her father began to call her several times on the phone," Boyce told reporters then. "She did not answer."
Boyce told reporters that Vetrano's father called a police chief who lives nearby. That person called emergency responders, and a search began.
After several hours searching in the woods alongside detectives, Phil Vetrano helped discover his daughter's body in marshland, police said.
A family friend told the New York Post that Phil Vetrano was "traumatised".
Soon after, he started a GoFundMe page to raise money to supplement a US$20,000 NYPD reward for information leading to the capture of his daughter's killer. The account has raised more than US$280,000.
"Turn yourself in," Vetrano begged his daughter's killer two weeks after her death. "I will make sure the reward money goes to the person of your choice. Your sister, your brother, your mother. It's a life-changer."
As weeks became months, the Vetrano family petitioned for the state to allow investigators to use familial DNA to try to find Vetrano's killer.
The technique had emerged in recent years as a way for investigators to search for "close-to-perfect matches" among relatives of a convict, The Washington Post reported in 2008.
However, the technique also attracted criticism and ethical questions from those who argue that family members could become "genetic informants" without consent. In New York state, familial DNA testing is not allowed.
In the end, it was a direct DNA match that led to an arrest.
"Could [familial DNA] have accelerated the investigation?" Boyce told reporters Sunday. "That's to be determined."
